fix(frontend): migrate to `NEXT_PUBLIC_FRONTEND_BASE_URL` (#10270)

## Changes 🏗️

We need to `FRONTEND_BASE_URL` to → `NEXT_PUBLIC_FRONTEND_BASE_URL`
given is needed on the new API client on the Front-end to make requests.
The `NEXT_PUBLIC` prefix is important so that it is available on the
client.

## Checklist 📋

#### For code changes:
- [x] I have clearly listed my changes in the PR description
- [x] I have made a test plan
- [x] I have tested my changes according to the test plan:
  - [x] Run the app locally
  - [x] The library and other pages work